I think that MIA is actually the most international of the US airports. It may not have the same number of international carriers as JFK or LAX but in terms of the sheer numbers of flights to Central and South America and the Caribbean, plus many to Europe, flown by American and international carriers, the proportion of international flights to domestic there is far higher than the others. In large part it results from its relatively isolated position at the tip of Florida whereas JFK and LAX are more centrally located relative to other major cities. ATL does not enter this race at all.

Actually from MIA, AA covers all of South America, Central America, Mexico City, Cancun and come November a large portion of their European routes with the addition of Manchester, UK to the daily Madrid, Paris, London Heathrow service out of MIA and I hear FCO and Brussels might be on the way.